Using ‘@’ for a directory name

Yes, this is a bit inconsistent, even within the GNU tools.

One problem with your proposal is that non-empty directories cannot be removed. Apart from that, -T (in GNU land, anyway) approximates what you want (the first case):

$ ls dira/ dirb/
dira/:
a

dirb/:
b
$ mv -iT dira/ dirb/
mv: overwrite `dirb/'? y
mv: cannot move `dira/' to `dirb/': Directory not empty
$ rm dirb/b 
$ mv -iT dira/ dirb/
mv: overwrite `dirb/'? y
$ ls dira/ dirb/
ls: cannot access dira/: No such file or directory
dirb/:
a

To see a listing, here are two variants, one that recurses into subdirectories and one that doesn't. All use syntax specific to bash, ksh and zsh.

comm -3 <(cd source && find -type f | sed 's/\.[^.]*$//' | sort) \
        <(cd dest && find -type f | sed 's/\.[^.]*$//' | sort)
comm -3 <(cd source && for x in *; do printf '%s\n' "${x%.*}"; done | sort) \
        <(cd dest && for x in *; do printf '%s\n' "${x%.*}"; done | sort)

Shorter, in zsh:

comm -3 <(cd source && print -lr **/*(:r)) <(cd dest && print -lr **/*(:r))
comm -3 <(print -lr source/*(:t:r)) <(print -lr dest/*(:t:r))

The comm command lists the lines that are common to two files (comm -12), that are only in the first file (comm -23) or that are only in the second file (comm -13). The numbers indicate what is subtracted from the output¹. The two input files must be sorted.

Here, the files are in fact the output of a command. The shell evaluates the <(…) construct by providing a “fake” file (a FIFO or a /dev/fd/ named file descriptor) as the argument to the command.

¹ _{So here the minus sayers are fully justified.}

If you want to perform actions on the files, you'll probably want to iterate over the source files.

cd source
for x in *; do
  set -- "…/dest/${x%.*}".*
  if [ $# -eq 1 ] && ! [ -e "$1" ]; then
    echo "$x has not been converted"
  elif [ $# -gt 1 ]; then
    echo "$x has been converted to more than one output file: " "$@"
  else
    echo "$x has been converted to $1"
  fi
done